Entanglement structure of the two-channel Kondo model

TL;DR

This paper investigates the entanglement properties of the two-channel Kondo model using a spin-chain approach and DMRG, confirming field theory predictions and identifying entanglement as an order parameter for quantum phase transitions.

Contribution

It introduces a spin-chain representation to analyze entanglement in the two-channel Kondo model and demonstrates how entanglement measures serve as order parameters for phase transitions.

Findings

Confirmed boundary entropy difference matches field theory predictions.

Showed impurity entanglement scales with characteristic length _{2CK}.

Identified tripartite entanglement near the critical point.

Abstract

Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel Kondo model to probe the ground-state block entropy, negativity, tangle, and Schmidt gap, using a density matrix renormalization group approach. In the presence of symmetric coupling to the two channels we confirm field-theory predictions for the boundary entropy difference, $\ln (g_{UV}/g_{IR})=\ln(2)/2$, between the ultraviolet and infrared limits and the leading $\ln(x)/x$ impurity correction to the block entropy. The impurity entanglement, $S_{\text{imp}}$, is shown to scale with the characteristic length $\xi_{2CK}$. We show that both the Schmidt gap and the entanglement of the impurity with one of the channels $-$ as measured by the negativity$-$ faithfully serve as order parameters for the impurity quantum phase transition appearing as a function of channel asymmetry, allowing for explicit determination of critical exponents, $\nu\!\approx\! 2$ and $\beta \!\approx\! 0.2$. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.